A novel construction of zero correlation zone sequences based on Boolean functions

Near-Optimal Zero Correlation Zone Sequence Sets from Paraunitary Matrices

“…We observe that the periodic correlation properties of the matrix C play an important role in the expanded form of PU matrix in order to construct ZCZ sequence sets. The matrix C is designed by the entries of the last two unitary matrices in the expanded form (9). Therefore, the ZCZ property of the constructed sequences depends on the specific structure of the individual row sequences of the unitary matrices.…”

“…In the literature, there are mainly three types of construction methods for ZCZ sequence sets. The first type is the direct construction method based on Boolean functions [8], [9]. The second type is based on perfect sequences [10], [11].…”

“…And the third type is based on MOCSSs [13], [14]. However, the sequence lengths and the set sizes for the constructions given in [8] and [9] are restricted to the powers of two only. In addition, for the constructions given in [10] and [11], the ZCZ parameters are limited by the existence of perfect sequences for the given number of phases.…”

“…Our proposed approach offers not only more choices in ZCZ parameter values compared to [8], [9], [10], and [11], but also provides a compact notation in treating matrix representations of multiple ZCZ sequence sets with performance parameter greater than 1/2. For example, a (3,81,18)-ZCZ sequence set given in Example 3 cannot be obtained by the previous works [8], [9], [10], and [11].…”

“…In the literature, ZCZ sequence sets have been constructed based on Boolean functions [8], [9], perfect sequences [10], [11], mismatched filtering [12], and so on. An important research direction is to generate ZCZ sequence sets based on complementary sets of sequences (CSSs) [13], [14].…”